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Reactive Power
The real power in ac circuits under steady conditions is the average of the instantaneous power taken over an integral number of half cycles and is expressed by
where Θ is the angle by which the current lags or leads the voltage. It is evident from Eq. 4101 and Figs. 48(b) and 48(c) that the real power in a purely inductive circuit is zero under steadystate conditions. However, the term reactive power is used to express the product of current and voltage in a circuit in which the real power is zero. In circuits where the current lags the voltage by an angle smaller than 90°, the reactive power consumed by the circuit is
In capacitive circuits the current leads the voltage, and the reactive power consumed by such a circuit is negative. Hence, capacitive circuits generate reactive power and are therefore sources of reactive power. Capacitors are used in industrial power systems to furnish reactive power. Thus, a circuit comprised of selfinductance, L, in series with a resistance R_{eff} has an impedance of
and
furthermore
From Eqs. 4104 and 4105 it follows that
from which


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